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The original was posted on /r/machinelearning by /u/WAIHATT on 2025-06-10 20:36:17+00:00.

Hi!

I’m a postdoc in Mathematics, but as you certainly know better than me, nowadays adding some ML to your research is sexy.

As part of a current paper I’m writing, I need to test several methods for solving inverse problems, and I have been asked by my supervisor to test also PINNs. I have been trying to implement a PINN to solve our problem, but for the love of me I cannot seem to make it converge.

Is this expected? Shouldn’t PINNs be good at inverse problems?

Just to give some context, the equation we have is not too complicated, but also not too simple. It’s a 2D heat equation, of which we need to identify the space-dependent diffusivity, k(x,y). So the total setup is:

• Some observations, data points in our domain, taken at different times

• k is defined, for simplicity, as a sum of two gaussians. Accordingly, we only have 6 parameters to learn (4 for the centers and 2 for the amplitudes), in addition to the PINNs weights and biases

• We also strongly enforce BC and IC.

But there is no way to make the model converge. Heck, even if I set the parameters to be exact, the PINN does not converge.

Can someone confirm me that I’m doing something wrong? PINNs should be able to handle such a problem, right?